Estimation of time-varying coherence functions

Two methods for computing an estimate of the time-varying magnitude squared (MS) coherence between two data sequences are described. The first method estimates the time-varying parameters of two autoregressive moving average (ARMA) transfer functions, whose product approximates the time-varying MS coherence function. The ARMA parameters are computed by an exponentially weighted recursive least squares algorithm. The second method estimates the time-varying MS coherence function by substituting time-varying estimates of the auto- and cross-spectra into usual the definition of the MS coherence function. The time-varying spectra are obtained by bandpass filtering, squaring and averaging operations.